A grinding machine includes a machine frame with a work piece support surface on which a work piece may be transporter through the machine. A grinding bar arrangement including two grinding shoes positioned in parallel is arranged transversely with respect to a work piece feeding direction across the width of the work piece support surface. The two grinding shoes carry a grinding medium on their surfaces facing the work piece support surface and are suspended via an eccentric drive. The two grinding shoes perform rotary movements in a plane parallel to the work piece support surface achieving a high quality grinding result.